Brian Arthur's vision of Complexity Economics

My friend Daria Roithmayr alerted me to a working paper of Brian Arthur laying out a vision for a new approach to studying economics. Brian Arthur is one of the pioneers of complex systems thought, and has devoted his life to understanding what really happens in our economy, and why this behavior is so different from what classical economics predicts.

Classical economics is a theory based on the concept of equilibrium. Equilibrium, in economics, is a state in which everyone is doing the best thing they could possibly do, relative to what everyone else is doing. And since everyone is doing the best possible thing, no one has incentive to change. So everything stays the same. Forever.

Okay, that doesn't sound much like our actual economy. So why is the equilibrium concept so central to economics? The answer is that equilibria can be calculated. If you make certain simplifying assumptions about how economic actors behave, you can prove that exactly one equlibrium exists, and you can calculate exactly what every actor is doing in this equilibrium. This allows economics to make predictions.

These predictions are useful in explaining many broad phenomena—for example, the relationship between supply, demand, and price. But they exclude any possibility of movement or change, and therefore exclude what is really interesting (and lucrative!) about the economy. Arthur explains it this way:

We could similarly say that in an ocean under the undeniable force of gravity an approximately equilibrium sea level has first-order validity. And this is certainly true. But, as with markets, in the ocean the interesting things happen
not at the equilibrium sea level which is seldom realized, they happen on the surface where ever-present disturbances cause further disturbances. That, after all, is where the boats are.

The vision of economics that Arthur lays out is based not on equilibrium, but on computation:

A better way forward is to observe that in the economy, current circumstances form the conditions that will determine what comes next. The economy is a system whose elements are constantly updating their behavior based on the present situation.
To state this in another way, formally, we can say that the economy is an ongoing computation—a vast, distributed,
massively parallel, stochastic one. Viewed this way, the economy becomes a system that evolves procedurally in a series
of events; it becomes algorithmic.

The part of this essay that was most challenging to me personally was where he talks about the limitations of mathematics:

...the reader may be wondering how the study of such computer-based worlds can qualify as economics, or what relationship this might have to doing theory. My answer is that theory does not consist of mathematics. Mathematics is a technique, a tool, albeit a sophisticated one. Theory is something different. Theory lies in the discovery, understanding, and
explaining of phenomena present in the world. Mathematics facilitates this—enormously—but then so does computation. Naturally, there is a difference. Working with equations allows us to follow an argument step by step and reveals conditions a solution must adhere to, whereas computation does not. But computation—and this more than compensates—allows us to see phenomena that equilibrium mathematics does not. It allows us to rerun results under different conditions, exploring when structures appear and don’t appear, isolating underlying mechanisms, and simplifying again and again to extract the bones of a phenomenon. Computation in other words is an aid to thought, and it joins earlier aids in economics—algebra, calculus, statistics, topology, stochastic processes—each of which was resisted in its time.

He later explains the limitations of mathematics with an analogy to biology:

Even now, 150 years after Darwin’s Origin, no one has succeeded in reducing to an equation-based system the process by which novel species are created, form ecologies, and bring into being whole eras dominated by characteristic species. The reason is that the evolutionary process is based on mechanisms that work in steps and trigger each other, and
it continually defines new categories—new species. Equations do well with changes in number or quantities within given
categories, but poorly with the appearance of new categories themselves. Yet we must admit that evolution’s central mechanisms are deeply understood and form a coherent group of general propositions that match real world observations, so these understandings indeed constitute theory. Biology then is theoretical but not mathematical; it is process-
based, not quantity-based. In a word it is procedural. By this token, a detailed economic theory of formation and
change would also be procedural. It would seek to understand deeply the mechanisms that drive formation in the economy and not necessarily seek to reduce these to equations.

Or, as Stuart Kauffman asked me when I told him about my mathematical biology research, "Can any of your equations predict rabbits fucking?"

Written by

Ben Allen

I am an assistant professor of mathematics at Emmanuel College in Boston, and a research associate at the Program for Evolutionary Dynamics at Harvard University. My research is in evolutionary game theory, mathematical modeling of cancer, and other topics in evolution and complex systems. benjcallen at gmail.